In spite of its many advantages, TDDFT also has limitations. By construction,
it is designed to simulate the time-evolution of the expectation value
\(\mathinner {\langle {\hat{A}}\rangle }\)  of one-body observables (TDHF) or two-body observables
(TDHFB, with some simplifications) [1]}, [2]}. It is not,
however, well adapted to describe the fluctuations of these observables, that
is, quantities \(\sigma ^{2}_{A} = \mathinner {\langle {\hat{A}^2}\rangle } - \mathinner {\langle {\hat{A}}\rangle }^2\) ; see
discussions in [3]}, [1]}, [5]}. This has practical
consequences: when solving the TDHFB equation with a broad range of initial
conditions at the beginning of the main fission valley in actinides, the
resulting trajectories tend to bundle and converge to very similar solutions
[6]}. In other words, TDHFB is very good at simulating the most
likely fission but does a poor job at exploring less likely fragmentations.
Different solutions have been proposed, including the stochastic mean field
[7]}, [8]}, [9]} or adding empirical terms to simulate
fluctuations and dissipation to the TDHFB equation [10]}. Another
route, which we will discuss in the next section, consists in adopting a
theoretical framework where collective correlations are explicitly included.
